A330103 Numbers whose prime-indices do not have weakly increasing numbers of prime factors, counted with multiplicity.

77, 119, 154, 217, 221, 231, 238, 287, 308, 357, 385, 403, 413, 434, 437, 442, 462, 469, 476, 533, 539, 551, 574, 581, 589, 595, 616, 651, 663, 693, 713, 714, 763, 767, 770, 779, 806, 817, 826, 833, 847, 861, 868, 871, 874, 884, 889, 893, 899, 924, 938

Offset

1,1

Comments

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

The sequence of terms together with their corresponding multisets of multisets begins:
   77: {{1,1},{3}}
  119: {{1,1},{4}}
  154: {{},{1,1},{3}}
  217: {{1,1},{5}}
  221: {{1,2},{4}}
  231: {{1},{1,1},{3}}
  238: {{},{1,1},{4}}
  287: {{1,1},{6}}
  308: {{},{},{1,1},{3}}
  357: {{1},{1,1},{4}}
  385: {{2},{1,1},{3}}
For example, 385 has prime indices {3,4,5} with numbers of prime factors (1,2,1), which is not weakly increasing, so 385 is in the sequence.

Mathematica

Select[Range[1000], !OrderedQ[PrimeOmega/@PrimePi/@First/@FactorInteger[#]]&]

Crossrefs

The version where prime factors are counted without multiplicity is A330281.

Cf. A001221, A001222, A056239, A112798, A302242, A330098, A330230, A330233.

Sequence in context: A235867 A274967 A229826 * A176278 A105998 A039444

Adjacent sequences: A330100 A330101 A330102 * A330104 A330105 A330106

Keyword

nonn

Author

Gus Wiseman, Dec 09 2019

Extensions

Term 667 deleted by Gus Wiseman, Feb 07 2021

Status

approved